COMPATIBILITY OF BIBLICAL CHRONOLOGY
WITH C-14 AGE

R. H. BrownYucaipa, California

Origins 21(2):66-79 (1994).

WHAT THIS ARTICLE IS ABOUT

The essential agreement between C-14 age and real time over the past
3000-3500 years is readily accounted for by the equilibrium inventory of C-14 that can be
expected to have been established in the Upper Biosphere within 1000-2000 years after the
Genesis Flood. With continuation of the present circumstances, the Lower Biosphere (ocean
below ~300 ft and associated sediment) cannot be expected to reach equilibrium status for
C-14 until more than 20,000 years into the future, but there is a reasonable model for
accumulation of the present total biosphere C-14 inventory within 5000 years since the
flood. Tree ring calibration of C-14 age data beyond 1500 BC presents a challenge of faith
for a choice between a biosphere model that accommodates the chronological data in the
Bible and one that has been developed without such restriction.
This article corrects deficiencies in previous treatments of C-14
dating by the author due to failure to recognize that published estimates for the
formation of C-14 are usually based on the assumption that the total biosphere is in
equilibrium (infinite age condition) for C-14. And it incorporates some recently published
data that are significant for placing C-14 age data within a biblical time frame.

INTRODUCTION

For over 40 years C-14 age data have been widely recognized as a
major challenge to a chronological framework that accommodates the historical data in
Genesis and Exodus. Much dedicated effort has been expended in the search for a biosphere
model that satisfactorily incorporates both the available data concerning C-14 inventory
and the chronological constraints derived from a straightforward historical-grammatical
exegesis of the Bible.1
As one who has experienced limited satisfaction and also frustration in
this effort, I offer the following as an additional contribution toward a satisfactory
treatment of the C-14 age problem in biblical creationism. At the outset I must express my
conviction that no treatment of C-14 age can establish the validity of the historical
details in the Bible. Evidence for the validity of those details must be accessible to
individuals who know nothing about C-14 and the sciences involved in C-14 dating. Our goal
is a scientifically acceptable explanation/interpretation of C-14 data from the
perspective of the Bible record.
Such explanation/interpretation must deal with three basic
considerations.

The average agreement between C-14 age and unquestioned real time age within about ±100
years over the past 3000 years (see Figure 1).

The current inventory of C-14 in the world's carbon exchange system  the
combination of upper and lower biosphere.

The dendrochronological calibration of C-14 ages extending to ~8000 years2
(and recently extended to ~22,000 years by U-Th disequilibrium dating4).

FIGURE 1. Dendrochronological calibration of C-14 age. Ordinates are the number of
years that must be added to a C-14 age to obtain its associated tree-ring calibrated age,
as specified on the abscissa. Data from References 2 and 3. BC/AD division is at 1950 BP.

AGREEMENT OF C-14 AGE WITH REAL-TIME AGE

Figure 1 is a plot of the difference between dendrochronological
(tree ring) calibrated age and the corresponding C-14 age over the range between 10 BP
(years before present) and 3999 BP, as given in the latest Calibration Issue of Radiocarbon.
The zero reference for the BP scale is 1950 AD. Accordingly 1950 BP corresponds to 0
BC/AD. The data in Figure 1 relate to the Upper Biosphere  air, soil, surface water,
mixed surface layer of the ocean, plant and animal life in this region, and organic
residuum which shares in an active interchange of carbon within the region. The actual
variations of the C-14/C-12 ratio in the Upper Biosphere have been less than might be
expected from the impression given by Figure 1. The highest and lowest points between 0
and 3000 BP represent, respectively, only +2.1% (2699 BP) and -2.5% (1420 BP) difference
between the age-corrected C-14/C-12 ratio in the sample and the carbon isotope ratio
standard reference. (The carbon isotope standard reference is indicated by line A in
Figure 4.)
The validity of the tree-ring master sequences on which the data for
Figure 1 is based is controlled by the availability of material which can be C-14 dated
and also has an unquestioned historical age. The time range from which such samples are
available extends to the vicinity of 3500 BP (~1500 BC).5 The essential
agreement between C-14 age and real time over this time range indicates an approximately
constant C-14/C-12 ratio in the reservoir from which the samples for C-14 dating have been
obtained. In other words, the Upper Biosphere has been in essential equilibrium (equal
C-14 input and output rates) over at least the past 3500 years.
C-14 enters the Upper Biosphere by diffusion and turbulence mixing from
the stratosphere where it is produced by cosmic radiation.5 Some C-14 is
eliminated from the Upper Biosphere by radioactive conversion to Nitrogen-14, but most
output is by transfer from the Mixed Surface Layer of the ocean to the Deep Ocean. Most of
the C-14 inventory is known to be in the Deep Ocean. The mean life of C-14 atoms before
conversion to N-14 is 8245 years,6 but the mean life of C-14 atoms in the Upper
Biosphere is only ~375 years. The 375-year estimate has been obtained from analysis of
changes in C-14/C-12 ratios resulting from nuclear weapon tests.7
When some entity is introduced into a reservoir at a constant rate R,
and has a mean life t in that reservoir, the
quantity q of this entity at any time t after initial
startup with q = 0 at t = 0 is given by the exponential
equation

q = Q (1 - e-t/t) (1)

in which e is the base of the natural logarithms, and Q
represents the equilibrium value of the entity represented by q. At
equilibrium Q = Rt, and

R = Q (1/t).
(2)

Ideally equilibrium is not attained until t becomes infinite, making
the last term in Equation (1) zero. For practical consideration, q = 0.99Q
when t = 4.6t. At t
= 3t, q has reached 95% of
its equilibrium value. These relationships are illustrated in Figure 2.

FIGURE 2. Exponential growth of a radioisotope at constant rate of formation.
Ordinates are percentage of equilibrium level. Equilibrium level Q is equal to the product
of the formation rate R and the mean lifetime t. Abscissae are
time as the number of mean lifetimes.

From these simple considerations one can conclude that if the Upper
Biosphere had a relatively insignificant C-14 concentration immediately after the flood
(Genesis 6-8), with ~375 years mean residence time C-14 in the Upper Biosphere would reach
95% of equilibrium concentration by ~1125 (=3×375) years after the flood. Practically
complete equilibrium would be attained in ~1725 years. Placing the flood at 5350 BP (3400
BC), according to the numerical data values in the Bible used by the New Testament church
(the Septuagint),8 essential equilibrium of C-14 in the Upper Biosphere would
have been established by 1675-2275 BC. The relatively small variations in the Upper
Biosphere C-14/C-12 ratio (differences in C-14 age with respect to real-time age) since
1500 BC are readily accounted for in terms of variation in the cosmic radiation shield
provided by the magnetic fields of the Earth and the Sun, and in the cosmic-ray particles
emitted by the Sun.9,10
The foregoing treatment indicates that if the generation rate of C-14
by cosmic ray interaction in the stratosphere, and the mean residence time of C-14 atoms
in the Upper Biosphere have been relatively constant since the flood, C-14 ages should be
in close agreement with corresponding real-time age over at least the past 3000 years, as
required by Consideration #1, and depicted in Figure 4C.

C-14 INVENTORY ACCUMULATION

Consideration #2 presents greater difficulty.
Fossil organic material (petroleum, coal, wood, shells, bone) from
geological horizons that reasonably must be interpreted as indicative of burial in the
Genesis flood episode, and is not a component of the modern biosphere, has less than 2% of
the modern concentration of C-14 in the Upper Biosphere.11
Estimates of the amounts of carbon in the various regions of the
biosphere, combined with measurements of the C-14/C-12 ratio in these regions, have
produced estimates of the modern C-14 inventory typically in the range between ~50,000 kg12
and ~75,000 kg.13 At the estimated C-14 production rates that have been
published in the scientific literature, e.g., 8.0 kg/yr in a recent publication,14
the "observed" C-14 inventory could not have been established by 5400 years
after the flood. At 8.0 kg/yr formation rate and 8245 years mean lifetime, Equations (1)
and (2) specify

q = 8.0 × 8245 (1 - e-5400/8245)
= 65,960 × 0.48 = 31,696 kg

for the biosphere, only 48% of a 66,000 kg equilibrium inventory (rounding 65,960 to
66,000).
In an effort to account for the biosphere C-14 inventory, I have
proposed that during the early centuries following the flood C-14 was produced much more
rapidly than at present (e.g., see Reference 15). This approach may be rendered
unnecessary by recognizing that the formation rates usually cited in the literature are
based on the assumption that the biosphere is in C-14 equilibrium, and the
additional assumption that the effective C-14 formation rate may be correctly estimated as
the quotient of the present inventory value and the mean life of C-14 atoms (Equation 2).
The 8.0 kg/yr production rate noted in the preceding paragraph is based on the assumption
that a present inventory of 66,000 kg represents equilibrium (66,000/8245 = ~8.0).
A first-order approximation model that is consistent with the biblical
data and the C-14 content of fossils from burial in the flood (less than 2% of the present
biosphere level) should specify that the total biosphere at present has reached only about
half (48% in the example immediately above) the C-14 equilibrium level. Ninety-five
percent of equilibrium level would not be reached until about 26,000 (=3×8245) years
after the flood. An appropriate estimate of the C-14 formation rate for such a model
should not be based on an assumption that present circumstances represent equilibrium.
A recent geophysics and climatology group investigation of the
distribution of C-14 produced by nuclear weapon tests indicates that previous estimates of
the amount of C-14 in the Lower Biosphere (deep ocean and sediments) have been excessive.7
As shown in Table 1 (row 1, columns 1 and 2) their estimate of the C-14 formation rate at
5.35 kg/yr is associated with a 44,100 kg estimate for the equilibrium inventory in the
total biosphere (44,100/8245 = 5.35).
Significant data that must be taken into account in the development of
a model for relating C-14 age to biblical chronology are given in Table 1.

A good estimate for the C-14 inventory in the contemporary Upper
Biosphere is 5599 kg.16 Since the other data in Table 1 are based on estimates
that might be classed as educated guesses (uncertainties as great as ~±20% are specified
in the original publications), 5600 kg is a suitable figure for column 3 of Table 1, and
all data in this table should be considered uncertain within at least ±20%. With the
uncertainty in determining the precise time since the flood from biblical specifications,
5000 years may be used as a satisfactorily approximate specification for this time, as
determined from the Septuagint text. The last column specifies the C-14 accumulation in
5000 years (45.5% of equilibrium level) at the rate given in the corresponding row of the
first column.
Column 4 lists Column 2 minus 5600, and column 5 minus 5600. Column 4
indicates the amount of the world inventory of C-14 that must be accounted for in the Deep
Ocean and its related sediments.
The data in row 4 are based on a C-14 formation rate estimate obtained
from data for cosmic ray intensity and geomagnetic field strength (Reference 10, Table V;
kg/yr = 3.74 × atoms/cm2/sec), and do not involve an uncertain assumption as
to whether the biosphere is or is not in equilibrium for C-14. For individuals who model
the biosphere on the basis of presumed equilibrium and unrestricted time, a C-14 formation
rate derived from an estimate of the equilibrium inventory is as significant as one
derived from estimates of factors associated with the primary production process. For a
model that specifies nonequilibrium, the only suitable C-14 formation rate estimate must
be based on nuclear reaction probabilities, cosmic ray intensity, and magnetic field
considerations.
The last row of Table 1 represents a biosphere C-14 exchange system
model that incorporates the chronological limitations obtained from the Bible. It is based
on the latest (1994) published estimate of the biosphere inventory (44,100 kg from
Reference 7), considered as a 5000-year accumulation, rather than as an equilibrium state.
(Compare row 1, column 2 with row 5, column 5.) This model requires an effective average
C-14 formation rate that is within a ±20% uncertainty range of the best estimate based on
cosmic ray intensity and geomagnetic field strength.
Taking extreme values for a ±20% uncertainty, Equations (1) and (2)
with a present inventory of 1.2 × 44,100 kg (from line 5, column 5), a formation rate of
0.8 × 10.2 kg/yr (from line 4, column 1), and t = 8245 years,
specify 12,734 years for buildup from a zero kg start to the postulated present inventory.
With these assumptions, particularly zero initial inventory, one can place ~13,000 years
as the maximum "real time" range that can be covered by C-14 age determinations.
To close the gap between the 11.9 and 10.2 kg/yr C-14 formation rates
on lines 5 and 4 of Table 1, a more complex model could allow for possible higher cosmic
ray intensity and/or lower geomagnetic field strength, with associated higher C-14
production rate, within the first two millennia following the flood. This model would
require a lower production rate over the last 3500 years in order to produce the C-14
accumulation associated with the 12 kg/yr average specified in row 5. An initially higher
production rate is reasonable in view of the cosmogenic nuclide (particularly
Beryllium-10) concentrations in ice cores from Greenland, and sediment cores from the
ocean, which indicate that at the height of the Ice Age C-14 production was at least 25%
higher than at present17 (greater Be-10 concentration per unit volume of ice in
a thin section of ice core), and ~20% higher at the end of the Ice Age (~10,000 BP C-14
age).18
Hence at this stage in the development of a model for the C-14 exchange
system a transiently higher C-14 formation rate may be postulated for the early centuries
following the flood, as depicted by Line B of Figure 3. With such specification the
requirement for a ~12 kg/yr average could be met with a modern formation rate closer to
the 10 kg/yr estimate based on cosmic ray and geomagnetic field intensities. The initial
portion of Line B represents the possibility that in order to provide greater protection
of organisms from cosmic ray damage, the geomagnetic field prior to the flood was stronger
than it has been over the last 3000 years. Line B of Figure 3 has been drawn only to
indicate possible change, and not to designate magnitudes or rates of change.

FIGURE 3. Biosphere Transition. Ordinates indicate suggested trends only, and are
arbitrary for both magnitude and scale. A: Total Active Biosphere Carbon. B: C-14
Formation Rate. C: Upper Biosphere C-14/C-12. Upper Biosphere equilibrium is presumed to
have been essentially established by 2000 yrs after the flood.

FIGURE 4. Upper Biosphere C-14/C-12 Ratio vs Time BP. Ordinates are first
approximation of C-14/C-12 ratio as percent of the modern reference value. A: C-14 age
based on equilibrium throughout all past time. B: C-14 age calibrated by tree rings and
coral. C: C-14 age calibrated by biblical chronology. Above (below) 100% ratio C-14 ages
are less (greater) than corresponding real-time age (see text). Concerning the range of
uncertainty for BP date of the flood and C-14/C-12 ratio at the time of the flood, see
References 8 and 11.

Line A  total biosphere carbon  in Figure 3 represents
the transfer of a large portion of the carbon inventory from the active exchange system to
a fossil state (coal, petroleum, fossil shell and bone, e.g.) at the time of the flood.
The trends depicted in Figure 3 for transition from pre-flood to modern conditions
accommodate both the first and second considerations specified previously on p. 67.

DENDROCHRONOLOGICAL CALIBRATION OF C-14 AGE

Master tree-ring sequences have been constructed for bristlecone
pine in the USA, and for oak and pine in Northern Europe. When extrapolated beyond the
range for which unquestioned historical records control the selection of ring overlap
between wood specimens, these sequences indicate that conventional C-14 ages at ~10,000 BP
are ~10% less than the corresponding real-time age as estimated by dendrochronology.2
Recent dating of Barbados coral by both C-14 and uranium-thorium series disequilibrium
techniques has extended this discrepancy to ~20% at 20,000 BP.4 These
extrapolations are represented by Line B in Figure 4. (A C-14/C-12 ratio greater
than the ratio on which C-14 ages are based  ratio greater than 100% 
represents a C-14 age less than the corresponding "real time" age.)
Their near-universal acceptance in scholarly circles presents a major challenge to a
chronological framework based on the Bible. As represented by Line B, C-14 ages beyond
~1500 BC are progressively less than the corresponding "real-time" age.
As represented by Line C, they are progressively much greater than the
corresponding "real-time" age.
The extension from coral dating can be questioned on the basis that
U-Th disequilibrium dating is based on the assumption that uranium and thorium isotope
ratios in seawater have always been the same as at present.19 Volcanism and
contact with fresh exposures of mineral surfaces during the crustal breakup associated
with the flood, and during continental relocation that probably occurred in early
post-flood time, would be expected to temporarily modify the traces of radioisotopes in
seawater. If there has been a transition to modern isotope ratios, U-Th disequilibrium
"ages" would have an unknown relationship with real time.
Some biblical creationists have tried to resolve the difficulty
associated with a sequence of as much as 8000 tree rings by suggesting that trees produced
multiple growth rings per year over several centuries following the flood. There may have
been many years in which more than one growth ring was produced at some locations, but the
production of as many as 4000 false "annual" rings over only 1500, or at most
2000, years is not a scientifically well-founded expectation. Extensive research beyond
what has been attempted so far would be required to find any support that might exist for
this suggestion.
The intellectual climate in which tree-ring master sequences have been
constructed favored selection of the longest sequence that could be justified. The use of
C-14 ages to roughly sequence a set of wood samples before "fine tuning" by ring
matching favored development of a master ring sequence that relates C-14 age to real-time
age on an approximate 1:1 basis, i.e., extension of the master dendrochronology scale to
about 8000 years, rather than the limit of ~5000 years to be expected from biblical
specifications. Individuals who include biblical testimony in their data base would seek
wood sample growth-ring overlaps that could be justified on a sound biological basis
without recourse to C-14 dating and also produced a minimal sequence. Given the subjective
aspect of tree-ring sequence matching, there is a possibility that a master sequence
developed from a biblical perspective would have a mathematical correlation coefficient
equally good, if not better, than do the master sequences that have become the current
standard for C-14 age calibration.
At least until someone with adequate qualifications attempts to develop
a 5000-year-limited master tree-ring sequence, the current dendrochronologic calibration
of C-14 ages will be a major test of faith for individuals who adhere to straightforward
historical-grammatical exegesis of the Bible. This is not blind faith, because there are
C-14 data that are incongruous on the basis of Curve B in Figure 4, but have clear
significance when interpreted in accord with Curve C. Examples of such data are given in
References 11 and 15.

CONCLUDING COMMENT

In full perspective there is a basis for confidence, and also room
for doubt, regarding compatibility between C-14 age data and the chronological data in the
Bible. For most individuals, selection between these options will be influenced by
predilection, rather than a decision based merely on the weight of evidence.

ACKNOWLEDGMENT

The author wishes to express appreciation for the suggestions from
unnamed pre-publication reviewers of this manuscript. The reader can thank them for many
improvements in readability and technical clarity.

APPENDIX I

While Figure 1 indicates that the C-14/C-12 ratio in the Upper
Biosphere has been approximately constant over the past 3000 years, it raises questions
concerning the trend for negative correction to C-14 age in the 0-200 and the 600-2400
year ranges. These trends are much greater than the minor variations due to the 11-year
cyclic pattern of cosmic ray output from the Sun.
The zero age reference for C-14 dating is the C-14/C-12 ratio that
would be expected in the Upper Biosphere if there had been no
"contamination" by carbon from the use of fossil fuels. Since fossil fuel (coal,
petroleum, and natural gas) contains £~1% of the C-14/C-12
ratio that characterizes the modern situation, the use of fossil fuel adds to
C-12 and reduces the C-14/C-12 ratio in the Upper Biosphere.
Plants and animals grown since the beginning of the Industrial
Revolution would at their zero age have had a lower C-14/C-12 ratio than the
reference C-14/C-12 ratio on which C-14 dating is based. Hence their C-14 age at present
will be greater than it would have been if there had been an insignificant use of
fossil fuel. This difference will be proportional to the accumulated consumption of fossil
fuel,20 as indicated by the left-most portion of Figure 1.
The negative correlation trend in the 600-2400 year range correlates
with long-term changes in the geomagnetic field.
C-14 production is inversely related to geomagnetic field intensity,
since the geomagnetic field deflects the primary cosmic rays, reducing the portion that
interacts with the stratosphere to form C-14. Direct measurements of the geomagnetic field
intensity over the time such capability has existed indicate that there has been a
steadily decreasing trend over the last 150 years. The remnant magnetism in
sediments and volcanic formations indicates that over an extended period prior to 2000 BP
the geomagnetic field intensity was increasing. Over the range from ~500 BP to
~3500 BP the geomagnetic intensity has been greater than it was at the beginning
of the Industrial Revolution.21 A greater geomagnetic field intensity
correlates with lower C-14 production, a lower C-14/C-12 ratio in the
biosphere, and C-14 ages greater than would have been the case if the geomagnetic
field had remained constant.

REFERENCES

Whitelaw RL. 1993. Radiocarbon dating after forty years: Do creationists see it
as supporting the Biblical Creation and Flood? Creation Research Society Quarterly
29(4):170-183. (See 30[3]:123,124 for comments.)

California woods. Our main article deals with Carbon-14 dating. Ancient wood is
commonly used for this dating technique, and, as discussed in this article, tree rings are
an important factor in calibrating Carbon-14 dates. Photo taken by Lenore Roth.